In the page that talks about comparing imaginary numbers (http://www.cut-the-knot.org/do_you_know/complex_compare.shtml) you mention and example where -1<1, you multiply by i, then i again and you get 1<(-1) -but by multiplying by i twice you are forgetting your inequality rules- you must switch the less than sign to be more then: ergo 1>(-1) and the property holds. Be careful.

No, there is no error.

With the reals you expect

(1) a < b and 0 < c imply ac < bc.

With the complex numbers, either assumption

0 < i or 0 < -i

leads to a contradiction if (1) is assumed to work in the complex case as well. Because, as you point out, i = -1. Which leads to a change of direction in the inequality. The trouble is this direction change is not implied by (1).